Vascular Cryptogam is an old botanical phrase, and it refers to those vascular plants that do not make seeds.  Thus, cryptogam (literally hidden gametophyte) refers to the production of a separate, usually very small, archegoniate gametophyte.  These are well represented in the fossil record.  Kenrick and Crane (1997) report that individual spores of land plants (these could be mosses, hornworts or vascular plants) have been found in the Lower Silurian (see the Geological Time Scale), a phase in the evolution of land plants that they refer to as "Eotracheophytic".  Unequivocal evidence of vascular land plants has been found in the mid Silurian, when the first radiation of tracheophytes occurred.  The early Devonian Period, however, saw an explosion in the diversity of early land plants which continued through the mid Permian, a time called the Eutracheophytic by Kenrick and Crane (1997).  In fact, we know so much about the diversity and structural details of the extinct taxa that taxonomic systems of the vascular cryptogams usually include them (e.g. Bold et al., 1987).  The wealth of fossil evidence from the Devonian to the present also provides the basis and support for the Telome Theory, a theory about the origins of all vascular plant organs from a simple dichotomizing axis (see Gorentz et al., 2002 for a good review of that theory).  Pearson (1995) explored the relationships between the green plants primarily by summarizing structural and developmental evidence.  His phylogenies relevant to the vascular cryptogams  include a diagram of the origin and early divergence and the fern taxa.  Rothwell (1999) examined 101 morphological characters of extinct and extant taxa from all major groups of vascular cryptogams.  His analysis supports the phylogenetic relationships that are assumed in Pearson (1995) and Bold et al. (1987).  Interpretations of relationships based on molecular evidence can be seen in a diagram from Pryer et al. (2001).  Combined structure, fossil, and molecular evidence can be seen in Tudge (2000) and the Tree of Life Project.  Clearly, as indicated by Bold et al. (1987) in the case of the vascular cryptogams "Nature mocks at human categories".   With that advice, I present a taxonomic system of the vascular cryptogam phyla that  roughly conforms to that of Bold et al. (1987) and Margulis and Schwartz (1998).  Those taxa that are marked with an asterisk (*) are extinct (as are all lower taxa within that taxon).   Orders are followed by representative genera.  

CLASS RHYNIOPSIDA

CLASS ZOSTEROPHYLLOPSIDA

CLASS TRIMEROPHYTOPSIDA

CLASS AGLOSSOPSIDA

CLASS GLOSSOPSIDA

PHYLUM PSILOTOPHYTA

CLASS PSILOTOPSIDA

CLASS SPHENOPSIDA

CLASS CLADOXYLIDOPSIDA

CLASS COENOPTERIDOPSIDA

CLASS OPHIOGLOSSOPSIDA

CLASS MARATTIOPSIDA

CLASS OSMUNDOPSIDA

CLASS FILICOPSIDA

CLASS MARSILIOPSIDA

CLASS SALVINIOPSIDA

CLASS PROGYMNOSPERMOPSIDA